with \({\mathbf {E}}\)  and \({\mathbf {B}}\)  the electric and magnetic fields. The first term corresponds to the well known electric dipole transition that changes by one unit the orbital angular momentum, leaving the spin wave function unchanged [1]}. One obtains
\({\cal M}^{ab}(Y_2 \rightarrow \gamma + X)&=&e Q_u~\langle X^a| \xi ^c|Y_2^b\rangle ~i\omega \epsilon ^c= \epsilon _{abc}~ \epsilon ^c~\frac{\omega }{\sqrt{6}}~\langle r \rangle _{2P\rightarrow 1S}\\\langle r \rangle _{2P\rightarrow 1S}&=&\frac{\int dr~[ y_{1S}(r)~ r ~y_{2P} (r)]}{\sqrt{\int dr~ y_{1S}(r)^2 \int dr~y_{2P}(r)^2}}\) 
